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A329704
Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).
1
1, 2, 5, 36, 54, 441, 473, 6525, 52577, 124025, 683820, 1513754, 1920552, 6079931, 6762923, 14751657, 17052782, 17310942, 36543714, 49919939, 60260967, 251849052, 364535720, 372476909, 562047389, 670395564, 670440852, 783856979, 824626800, 1084201689, 1122603809
OFFSET
1,2
COMMENTS
Are 1 and 36 the only terms that are also triangular numbers?
No other triangular terms up to A000217(10^8). - Michel Marcus, Mar 01 2020
LINKS
EXAMPLE
5 is a term since sigma(5) = 6 and sigma(5) - 5 = 1 are both triangular numbers.
MATHEMATICA
triQ[n_] := IntegerQ @ Sqrt[8*n+1]; Select[Range[10^5], triQ[(s = DivisorSigma[1, #])] && triQ[s - #] &]
PROG
(PARI) isok(k) = my(s=sigma(k)); ispolygonal(s, 3) && ispolygonal(s-k, 3); \\ Michel Marcus, Feb 29 2020
CROSSREFS
Intersection of A045745 and A045746.
Sequence in context: A309667 A059586 A160968 * A275552 A086832 A317801
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 28 2020
STATUS
approved